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A random sample is drawn from a population with mean μ = 74 and standard deviation...

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Basic Math

A random sample is drawn from a population with mean μ= 74 and standard deviation σ = 6.2. [You may findit useful to reference the z table.]

a. Is the sampling distribution of the samplemean with n = 18 and n = 47 normallydistributed?

Yes, both the sample means will have a normal distribution.

No, both the sample means will not have a normaldistribution.

No, only the sample mean with n = 18 will have a normaldistribution.

No, only the sample mean with n = 47 will have a normaldistribution.

b. Calculate the probability that the samplemean falls between 74 and 77 for n = 47. (Roundintermediate calculations to at least 4 decimal places,“z” value to 2 decimal places, and final answer to 4decimal places.)

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